Mathematics Graduate Courses

MATH 5090.Topics in the Foundations of Mathematics. Various topics. Prerequisite: MATH 3000 and consent of instructor.

MATH 5100.Seminar in Elementary School Mathematics. A course to give graduate students in mathematics educa­tion, or in-service teachers, an in-depth view of new contents, materials, and strategies for teaching mathematics in elementary schools. The course is primarily designed to meet the needs of students working towards M.S.N.S., M.S.T., M.A.T. degrees. Prerequisite: 6 hours of MATH 4100.

MATH 5110. Modeling Flow Transport in Soil and Groundwater Systems.Mathematical models are formulated and applied to simulate water flow and chemical transcript in soil and groundwater systems. Soil spatial variability and heterogeneity are considered in the model­ing processes. Using and comparing models, students obtain the capability to transfer a physical problem to a mathematical model, to use numerical methods, such as the finite element methods, to solve the mathematical problem, and to correctly interpret the numeri­cal outputs. Students develop and program numerical solutions for select problems and utilize existing codes for modeling a variety of comprehensive problems. Cross listed with SOIL 5110.

MATH 5140. Numbers, Operations, and Patterns for the Middle-level Learner.Provides working middle-level mathematics teach­ers opportunities to understand and discuss numbers, their representations, and operations on them from an abstract perspective that includes elegant proof. Also emphasized is the role of language and purpose in compos­ing definitions. Cross listed with NASC 5140. Prerequisites: admission to a university graduate program, in either degree or non-degree seeking status, and acceptance into Middle-level Mathematics Program.

MATH 5160. Social and Historical Issues in Math­ematics and the Middle-Level Learner.Empowers teachers of middle-level mathematic­ics to design more engaging experiences. Em­phasizes the historical context for the develop­ment of mathematics, especially its symbols, tools, personalities, and classic problems. Cross listed with NASC 5160. Prerequisites: admission to a UW graduate program, in either degree or non-degree seeking status, and acceptance into the Middle-level Mathematics Program.

MATH 5170. Connecting Geometry with Problem- Solving for the Middle-Level Learner.Showcases two aspects of 2D and 3D geometry: measurement and transformation. Emphasis reflects current state and national standards for middle-level mathematics class­room and teacher preparation, especially ap­propriate uses of technology, geometric tools, mathematical language, and problem-solving strategies. Cross listed with NASC 5170. Pre­requisites: admission to a university graduate program, in either degree or non-degree seek­ing status, and acceptance into the Middle-level Mathematics Program.

MATH 5190. Mathematics of Change and the Middle-Level Learner. Students gain a solid understanding of data and functions in the service of calculus. Course is hands-on, project-driven and focuses on the essential concepts of functions and calculus and their role in middle-level mathematics. Emphasis is on writing and technology (calculators and probeware). Cross listed with NASC 5190. Prerequisites: admission to a UW graduate pro­gram, in either degree or non-degree seeking status, and acceptance into the Middle-level Mathematics Program.

MATH 5400: Methods of Applied Mathematics I.First semester of a one-year survey of topics and methods of applied mathematics, with emphasis on applications from physics and engineering. The full sequence includes introductions to mathematical aspects of me­chanics (e.g., conservation laws), asymptotic expansions, systems of ODE and stability, integral equations and calculus of variations, PDE with boundary value problems and gen­eralized solutions (including wave, heat, and potential equations), numerical methods and stability. Prerequisite: MATH 2250, 4200 or 4400, and 2310 or 4430.

MATH 5570: Matrix Theory and Combinatorics.An overview of matrix theory and its ap­plications to combinatorics. Topics include Smith normal form, the Perron-Frobenius theory of non-negative matrices, location and perturbation of eigenvalues, and interlacing of eigenvalues. Applications include structure theorums for (0,1)-matrices, network flows, spectra of graphs, and the permanent. Prereq­uisite: MATH 5500.

MATH 5600: Point-Set Topology.Topics con­sidered are metric spaces, open spheres, open sets, closed sets, continuous functions, limit points, topological spaces, homeomorphisms, compactness, connectedness, and separability. The familiar notion of distance on the real number line is generalized to the notion of a metric for an arbitrary set, which is in turn generalized to the concept of a set topology for a set. Certain applications to analysis and geometry are indicated. Prerequisite: MATH 3000 and 4200.

MATH 5959: Enrichment Studies.Designed to provide an enrichment experience in a variety of topics. Note: credit in this course may not be included in a graduate Program of Study for degree purposes.

MATH 5960: Thesis Research.Graduate level course designed for students who are involved in research for their thesis project. Also used for students whose course­work is complete and are writing their thesis. Prerequisite: enrollment in a graduate degree program.

MATH 5980: Dissertation Research.Graduate level course designed for stu­dents who are involved in research for their dissertation project. Also used for students whose coursework is complete and are writing their dissertation. Prerequisite: enrollment in a graduate level degree program.